This invention relates in general to the field of crystal resonators, and more particularly to methods of determining the angles-of-cut of doubly rotated crystal resonators.
The frequency vs. temperature (xe2x80x9cf vs. Txe2x80x9d) characteristics of crystal resonators depend on the angles of cut of the quartz plate with respect to the crystallographic axes. In certain applications, an accuracy within seconds of arc is required. Due to imperfections in both the cutting techniques and the quartz, the angles of cut of each blank must be measured, the blanks must be sorted, and, if necessary, angle-corrected to achieve the required angles-of-cut precision.
X-ray diffraction is the standard technique for measuring angles-of-cut, and double-crystal X-ray diffraction is generally used to measure the angles between the major surface of a blank and a specified set of atomic planes. In this technique, X-rays are reflected from atomic planes in a crystal in accordance with Bragg""s law: nxcex=2d sin xcex8xcex2, where xcex is the wavelength of the reflected X-rays and xcex8xcex2=the xe2x80x9cBragg angle,xe2x80x9d the angle at which the peak of the reflection occurs. References on the X-ray techniques are J. L. Chambers, xe2x80x9cAn Instrument for Automated Measurement of the Angles of Cut of Doubly Rotated Quartz Crystals,xe2x80x9d 37th Annual Symposium on Frequency Control, 1983, pp 275-283 and J. L. Chambers, et al., xe2x80x9cAn Instrument for Automated Measurement of the Angles of Cut of Doubly Rotated Quartz Crystals,xe2x80x9d 35th Annual Symposium On FrequencyControl, 1981, pp. 60-70. In most X-ray orientation systems, the Kxcex1 radiation from a copper target is used because the wavelength of this radiation is near the typical atomic spacings.
Referring now to FIG. 1, which illustrates double-crystal X-ray diffraction, the monochromator crystal collimates the X-rays, allowing more accurate determination of the Bragg angle than is possible with single-crystal orientation systems. The goniometer allows varying the angle of incidence of the X-rays and determining the angle of maximum reflection. When a laser is used to define the plane of the blank, a measurement precision of xcx9c2 seconds of arc is possible. Also, the X-ray and goniometer techniques can be combined in an X-ray goniometer as described in Knolmayer xe2x80x9cX-Ray Goniometer of the Modified Doubly Rotated Cuts,xe2x80x9d 35th Annual Symposium On Frequency Control, 1981, pp. 567. Other priors art techniques are based on an automated piezogonimeter described in Kobayashi, xe2x80x9cFully Automated Piezogoniometer (Automatic Quartz Plate Classifier),xe2x80x9d 32nd Annual Symposium on Frequency Control, 1978: p 317-320.
The AT angle-of-cut presents a different problem not addressed by prior art techniques. The AT-cut is the most commonly used zero temperature coefficient (xe2x80x9cZTCxe2x80x9d) thickness shear mode resonator. The AT-cut""s angles of cut are about xcex8=35xc2x015xe2x80x2xc2x130xe2x80x2 and xcfx86=0xc2x0, as depicted in FIG. 2. The xcex8 angle is the primary determinant of the resonator""s f vs. T characteristic. Therefore, it is intentionally adjusted to a precise value typically within the xc2x130xe2x80x2 range, depending on the application. The xcfx86 angle is usually not measured during manufacturing operations for two reasons. First, a small error in the xcfx86 angle generally has only small effects on the f vs. T characteristic of the resonator. Secondly, the equipment needed to measure both xcex8 and xcfx86 angles is quite expensive, with an average cost exceeding $100,000 per instrument. The prior art X-ray diffraction and goniometer methods are particularly unsuitable for measuring errors in the xcfx86 angle, because their errors are not always small, and even small xcfx86 angle errors are not negligible for certain applications. For example, errors in the xcfx86 angle can result in significant manufacturing yield problems. Such errors also effect properties such as the AT-cut""s sensitivity to electric fields, i.e., when xcfx86=0xc2x0, the AT-cut is insensitive to electric fields, but when xcfx86xe2x89xa00xc2x0, the AT-cut exhibits a finite sensitivity to electric fields. Prior art techniques are generally not satisfactory and are costly. There are no known inexpensive techniques for measuring the deviations from xcfx86=0xc2x0. Thus, there has been a long-felt need to determine inexpensively whether the xcfx86 angle deviates from xcfx86=0xc2x0.
The inventors have observed that the effects of c-modes"" displacement ratio i.e. the ratio of out-of-plane to in-plane displacement, variations with xcfx86 angle can be used to determine deviations from xcfx86=0xc2x0. They have observed a direct relationship between deviation from xcfx86=0xc2x0 and the c-mode displacement ratio, so that the larger the deviation from xcfx86=0xc2x0, then the larger is the change in the normalized frequency of the c-mode upon immersion in, or contact with, a fluid. Thus, xcfx86 angle deviations are determined by measuring xcex8 and xcfx86 angles of standard resonators with different small xcfx86 angles, i.e. less than or equal to 7xc2x0, and their quasi-pure mode frequencies in ambient air and a test fluid, calculating the normalized frequency changes between the air and fluid measurements, measuring the test resonator in air and then in fluid, and then comparing the results. Accordingly, this invention fulfills the long-felt need to determine inexpensively xcfx86 angle deviation by providing methods of determining the xcfx86 angle-of-cut, which do not suffer from the disadvantages, shortcomings and limitations of the current expensive, time-consuming and cumbersome testing equipment. Other useful prior art references are:
J. Clastre et al. xe2x80x9cGoniometric Measurements of the Angles of Cut of Doubly Rotated Quartz Plates,xe2x80x9d Proc. 32 th Ann. Symposium on Frequency Control, pp. 310-316, 1978;
J. F. Darces et al., xe2x80x9cFinal X-Ray Control of the Orientation of Round or Rectangular Quartz Slides for Industrial Purposes,xe2x80x9d Proc. 32 th Ann. Symposium on Frequency Control, pp. 304-309, 1978;
V. E. Bottom, Introduction to Quartz Crystal Unit Design, Van Nostrand Reinhold Company, Chapter 11, 1982;.
J. A. Kusters, xe2x80x9cResonator and Device Technology,xe2x80x9d in E. A. Gerber and A. Ballato; Precision Frequency Control, Vol. 1, pp.161-183, Academic Press, 1985;
C. A. Adams et al., xe2x80x9cX-Ray Technologyxe2x80x94A Review,xe2x80x9d Proc. 41 st Ann. Symposium on Frequency Control, pp. 249-257, 1987; and
H. Bradaczek, xe2x80x9cAutomated X-Ray Sorting Machine For Round Quartz Blanks,xe2x80x9d Proc. 45 th Ann. Symposium on Frequency Control, pp. 114-116, 1991.
It is therefore one object of the present invention to provide methods and techniques to determine whether the xcfx86 angle deviates from xcfx86=0xc2x0 based on the quasi-pure modes"" displacement ratio variations with the xcfx86 angle.
It is another object of the present invention to provide methods and techniques to determine whether the xcfx86 angle deviates from xcfx86=0xc2x0 based on the c-modes"" displacement ratio variations with the xcfx86 angle.
It is still another object of this invention to provide methods and techniques to determine whether the xcfx86 angle in a near AT angle-of-cut deviates from xcfx86=0xc2x0 based on the c-modes"" displacement ratio variations with the xcfx86 angle.
It is yet another object of this invention to provide methods and techniques to determine whether the xcfx86 angle in a near BT angle-of-cut deviates from xcfx86=0xc2x0 based on the b-modes"" displacement ratio variations with the xcfx86 angle.
It is still a further object of this invention to provide methods and techniques to determine whether the xcfx86 angle in the LGX family of rotated-y-cut ZTC crystal resonators deviates from xcfx86=0xc2x0 based on the quasi-shear modes"" displacement ratio variations with the xcfx86 angle. The term xe2x80x9cLGXxe2x80x9d is well-known to those skilled in the art as a shorthand expression for a family of piezoelectric crystals, including the langasite (LGS), langanite (LGN), langatate (LGT) and so on.
To attain these and other objects and advantages, the present invention provides methods for determining deviations from xcfx86=0xc2x0 in test resonators based on the quasi-pure modes"" displacement ratio variations with xcfx86 angle. The method comprises measuring xcex8 and xcfx86 angles in reference resonators with different small xcfx86 angles and quasi-pure mode frequencies of reference resonators in both ambient air and a test fluid, calculating the normalized frequency changes between the air and fluid measurements as a reference point, measuring the test resonator in air then in fluid and comparing the results. Also contemplated are similar methods for measuring the xcfx86 angles in the quasi-pure mode of near-BT-cut resonator plates and the LGX family of rotated-y-cut ZTC crystal resonators, so that the appropriate modes"" displacement ratio variations with the xcfx86 angle determine deviations from xcfx86=0xc2x0. It is well-known in the resonator art that the designations xe2x80x9ccxe2x80x9d and xe2x80x9cbxe2x80x9d modes simply refer to the uncoupled, or pure, mode that exists in rotated Y cuts of crystals having group point symmetry 32. Departure from the xcfx86=0xc2x0 condition introduces a slight coupling of the modes, so that the pure mode becomes xe2x80x9cquasi-pure, with an admixture of out-of-plane motions that increase with the increasing xcfx86 value. The methods of this invention are based on the principle that the larger the deviation from xcfx86=0xc2x0, the larger is the change in the normalized frequency of the quasi-pure mode upon immersion into a fluid. In the preferred embodiment of the methods of this invention the test fluid used for measuring a reference fluid quasi-pure mode frequency is pure water at ambient temperature. Temperature can affect the results, so preferably, the measurements on the reference resonators and test resonators are made at the same temperature. If the measurements are not made at the same temperature, then errors on the order of 1 ppm per degree C. can result. This compares with the normalized frequency changes on the order of a 100 ppm per degree change in Q-angle. For known xcex8 angles, it is possible to compensate for the effects of temperature.
The exact nature of this invention, as well as other objects and advantages thereof, will be readily apparent from consideration of the following specification relating to the annexed drawings.